Thanks to Warren and Josef for their time and thoughts. I feel like I
now understand the underlying problem and have some good options to
solve my short term issues (I assigned the project last night and they
need to be able to start working on it immediately). I actually use a
TransferFunction class that derives from ltisys. I could override its
lsim2 method to try out some of these solutions quickly and fairly
easily.
Ryan
On Thu, Jan 28, 2010 at 10:00 PM, <josef.pktd@gmail.com> wrote:
> On Thu, Jan 28, 2010 at 10:33 PM, Warren Weckesser
> <warren.weckesser@enthought.com> wrote:
>>josef.pktd@gmail.com wrote:
>>> On Thu, Jan 28, 2010 at 8:50 PM, Warren Weckesser
>>> <warren.weckesser@enthought.com> wrote:
>>>>>>> Ryan,
>>>>>>>> The problem is that the ODE solver used by lsim2 is too good. :)
>>>>>>>> It uses scipy.integrate.odeint, which in turn uses the Fortran library
>>>> LSODA. Like any good solver, LSODA is an adaptive solver--it adjusts its
>>>> step size to be as large as possible while keeping estimates of the error
>>>> bounded. For the problem you are solving, with initial condition 0, the
>>>> exact solution is initially exactly 0. This is such a nice smooth solution
>>>> that the solver's step size quickly grows--so big, in fact, that it skips
>>>> right over your pulse and never sees it.
>>>>>>>> So how does it create all those intermediate points at the requested time
>>>> values? It uses interpolation between the steps that it computed to create
>>>> the solution values at the times that you requested. So using a finer grid
>>>> of time values won't help. (If lsim2 gave you a hook into the parameters
>>>> passed to odeint, you could set odeint's 'hmax' to a value smaller than your
>>>> pulse width, which would force the solver to see the pulse. But there is no
>>>> way to set that parameter from lsim2.)
>>>>>>>>>> It's something what I suspected. I don't know much about odeint, but
>>> do you think it would be useful to let lsim2 pass through some
>>> parameters to odeint?
>>>>>>>>>> Sounds useful to me. A simple implementation is an optional keyword
>> argument that is a dict of odeint arguments. But this would almost
>> certainly break if lsim2 were ever reimplemented with a different
>> solver. So perhaps it should allow a common set of ODE solver
>> parameters (e.g. absolute and relative error tolerances, max and min
>> step sizes, others?).
>>>> Perhaps this should wait until after the ODE solver redesign that is
>> occasionally discussed:
>>http://projects.scipy.org/scipy/wiki/OdeintRedesign>> Then the solver itself could be an optional argument to lsim2.
>> I was just thinking of adding to the argument list a **kwds argument
> that is directly passed on to whatever ODE solver is used. This should
> be pretty flexible for any changes and be backwards compatible.
>> I've seen and used it in a similar way for calls to optimization
> routines, e.g. also optimize.curve_fit, does it. What are actually
> valid keywords would depend on which function is called.
>> (But I'm not a user of lsim, I'm just stealing some ideas from lti and
> friends for time series analysis.)
>> Josef
>>>>>>>> Warren
>>>>> Josef
>>>>>>>>>>>>> The basic problem is you are passing in a discontinuous function to a solver
>>>> that expects a smooth function. A better way to solve this problem is to
>>>> explicitly account for the discontinuity. One possibility is the attached
>>>> script.
>>>>>>>> This is an excellent "learning opportunity" for your students on the hazards
>>>> of numerical computing!
>>>>>>>> Warren
>>>>>>>>>>>> Ryan Krauss wrote:
>>>>>>>>> I believe I have discovered a bug in signal.lsim2. I believe the
>>>>> short attached script illustrates the problem. I was trying to
>>>>> predict the response of a transfer function with a pure integrator:
>>>>>>>>>> g
>>>>> G = -------------
>>>>> s(s+p)
>>>>>>>>>> to a finite width pulse. lsim2 seems to handle the step response just
>>>>> fine, but says that the pulse response is exactly 0.0 for the entire
>>>>> time of the simulation. Obviously, this isn't the right answer.
>>>>>>>>>> I am running scipy 0.7.0 and numpy 1.2.1 on Ubuntu 9.04, but I also
>>>>> have the same problem on Windows running 0.7.1 and 1.4.0.
>>>>>>>>>> Thanks,
>>>>>>>>>> Ryan
>>>>> ------------------------------------------------------------------------
>>>>>>>>>> _______________________________________________
>>>>> SciPy-User mailing list
>>>>>SciPy-User@scipy.org>>>>>http://mail.scipy.org/mailman/listinfo/scipy-user>>>>>>>>> from pylab import *
>>>> from scipy import signal
>>>>>>>>>>>> g = 100.0
>>>> p = 15.0
>>>> G = signal.ltisys.lti(g, [1,p,0])
>>>>>>>> t = arange(0, 1.0, 0.002)
>>>> N = len(t)
>>>>>>>> # u for the whole interval (not used in lsim2, only for plotting later).
>>>> amp = 50.0
>>>> u = zeros(N)
>>>> k1 = 50
>>>> k2 = 100
>>>> u[k1:k2] = amp
>>>>>>>> # Create input functions for each smooth interval. (This could be simpler,
>>>> since u
>>>> # is constant on each interval.)
>>>> a = float(k1)/N
>>>> b = float(k2)/N
>>>> T1 = linspace(0, a, 201)
>>>> u1 = zeros_like(T1)
>>>> T2 = linspace(a, b, 201)
>>>> u2 = amp*ones_like(T2)
>>>> T3 = linspace(b, 1.0, 201)
>>>> u3 = zeros_like(T3)
>>>>>>>> # Solve on each interval; use the final value of one solution as the
>>>> starting
>>>> # point of the next solution.
>>>> # (We could skip the first calculation, since we know the solution will be
>>>> 0.)
>>>> (t1, y1, x1) = signal.lsim2(G,u1,T1)
>>>> (t2, y2, x2) = signal.lsim2(G, u2, T2, X0=x1[-1])
>>>> (t3, y3, x3) = signal.lsim2(G, u3, T3, X0=x2[-1])
>>>>>>>> figure(1)
>>>> clf()
>>>> plot(t, u, 'k', linewidth=3)
>>>> plot(t1, y1, 'y', linewidth=3)
>>>> plot(t2, y2, 'b', linewidth=3)
>>>> plot(t3, y3, 'g', linewidth=3)
>>>>>>>> show()
>>>>>>>> _______________________________________________
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